Relative Angular Momentum in 2 Body Decay at Detector Level

How the relative angular momentum of two particles can be detect by detector in two particle decay (center of mass frame)? I am curious about the signatures/differentiation between different relative momenta, means how one can decide that it is L=0, L=1,2,3,....?

Of course the distribution would be different, but what kind of difference exist exactly? Looking for some pictorial spirit to understand the difference.

For example an [itex]L=0[/itex] particle will be independent from [itex]\theta= - \pi [/itex] to [itex]\pi[/itex] (or [itex] \cos \theta \in [-1,1][/itex].
An [itex]L=1[/itex] will have some particular dependence on theta..

I don't know maybe there are other more effective ways to do that in a detector.

But in theoretical calculation I am not clear what is the major difference I should have to keep in mind in calculating these partial decay widths. I know in the final result there must be projection on some [itex]Y^m_{l}[/itex] but I am not able to get the difference from start. Do you have any idea?